CP Violation in $B^\pm\to ρ^0π^\pm$ and $B^\pm\to σπ^\pm$ Decays

Hai-Yang Cheng

paper

CP Violation in $B^{\pm} \to ρ^{0} π^{\pm}$ and $B^{\pm} \to σ π^{\pm}$ Decays

arXiv:2005.06080

Abstract

The decay amplitude of $B^{+} \to π^{+} π^{-} π^{+}$ in the Dalitz plot has been analyzed by the LHCb using three different approaches for the $S$ -wave component. It was found that the mode with $σ$ (or $f_{0} (500)$ ) exhibited a CP asymmetry of 15\% in the isobar model, whereas the $f_{2} (1270)$ mode had a 40\% asymmetry. On the contrary, CP asymmetry for the dominant quasi-two-body decay $B^{-} \to ρ^{0} π^{-}$ was found to be consistent with zero in all three approaches, while all the existing theoretical predictions lead to a negative CP asymmetry ranging from $- 7%$ to $- 45%$ . We show that the nearly vanishing CP violation in $B^{-} \to ρ^{0} π^{-}$ is understandable in the framework of QCD factorization (QCDF). It arises from the $1/ m_{b}$ power corrections to the penguin amplitudes due to penguin annihilations and to the color-suppressed tree amplitude due to hard spectator interactions. Penguin annihilation and hard spectator interactions contribute destructively to $A_{C P} (B^{-} \to ρ^{0} π^{-})$ to render it consistent with zero. The branching fraction and CP asymmetry in $B^{-} \to σ / f_{0} (500) π^{-}$ are investigated in QCDF with results in agreement with experiment.

arXiv comment11 pages

CP Violation in B±→ρ0π± and B±→σπ± Decays

Abstract

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CP Violation in $B^{\pm} \to ρ^{0} π^{\pm}$ and $B^{\pm} \to σ π^{\pm}$ Decays